Question

find the measure of each indicated angle.
1)
2)
3)
4)
5)
6)
7)
8)
9)

Explanation:

Step1: Use angle subtraction for \(m\angle UVX\)

\(m\angle UVX = 148^{\circ}- 32^{\circ}\)

Step2: Calculate \(m\angle UVX\)

\(m\angle UVX=116^{\circ}\)

Step3: Use vertical angles for \(m\angle PTQ\)

Vertical angles are equal. So \(m\angle PTQ = 72^{\circ}\)

Step4: Use supplementary angles for \(m\angle LON\)

Supplementary angles sum to \(180^{\circ}\). So \(m\angle LON=180^{\circ}-60^{\circ}\)

Step5: Calculate \(m\angle LON\)

\(m\angle LON = 120^{\circ}\)

Step6: Use supplementary angles for \(m\angle MNL\)

Supplementary angles sum to \(180^{\circ}\). So \(m\angle MNL=180^{\circ}-49^{\circ}\)

Step7: Calculate \(m\angle MNL\)

\(m\angle MNL = 131^{\circ}\)

Step8: Use supplementary angles for \(m\angle TW V\)

Supplementary angles sum to \(180^{\circ}\). So \(m\angle TW V=180^{\circ}-23^{\circ}\)

Step9: Calculate \(m\angle TW V\)

\(m\angle TW V = 157^{\circ}\)

Step10: Use angle addition for \(m\angle DBC\)

Assuming \(\angle ABC = 90^{\circ}\) (right - angle), \(m\angle DBC=45^{\circ}+ \angle ABD\). If \(\angle ABD\) is part of a right - angle and \(\angle ABD = 45^{\circ}\), \(m\angle DBC = 90^{\circ}\)

Step11: Use supplementary angles for \(m\angle YXZ\)

Supplementary angles sum to \(180^{\circ}\). So \(m\angle YXZ=180^{\circ}-119^{\circ}\)

Step12: Calculate \(m\angle YXZ\)

\(m\angle YXZ = 61^{\circ}\)

Step13: Use angle addition for \(m\angle EFG\)

\(m\angle EFG=44^{\circ}+107^{\circ}\)

Step14: Calculate \(m\angle EFG\)

\(m\angle EFG = 151^{\circ}\)

Step15: Use vertical angles for \(m\angle RUS\)

Vertical angles are equal. If the angle opposite to \(160^{\circ}\) is supplementary to \(m\angle RUS\), and vertical angles: \(m\angle RUS = 20^{\circ}\) (since \(180 - 160=20\))

Answer:

1. \(116^{\circ}\)
2. \(72^{\circ}\)
3. \(120^{\circ}\)
4. \(131^{\circ}\)
5. \(157^{\circ}\)
6. \(90^{\circ}\)
7. \(61^{\circ}\)
8. \(151^{\circ}\)
9. \(20^{\circ}\)